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Steric 6 cubes

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Steric 6-cubes

In six-dimensional geometry, a steric 6-cube is a convex uniform 6-polytope. There are unique 4 steric forms of the 6-cube.

Contents

Alternate names

  • Runcinated demihexeract/6-demicube
  • Small prismated hemihexeract (Acronym sophax) (Jonathan Bowers)

    • Cartesian coordinates

    The Cartesian coordinates for the 480 vertices of a steric 6-cube centered at the origin are coordinate permutations:

    (±1,±1,±1,±1,±1,±3)

    with an odd number of plus signs.

    Alternate names

  • Runcitruncated demihexeract/6-demicube
  • Prismatotruncated hemihexeract (Acronym pithax) (Jonathan Bowers)

    • Cartesian coordinates

    The Cartesian coordinates for the 2880 vertices of a stericantic 6-cube centered at the origin are coordinate permutations:

    (±1,±1,±1,±3,±3,±5)

    with an odd number of plus signs.

    Alternate names

  • Runcicantellated demihexeract/6-demicube
  • Prismatorhombated hemihexeract (Acronym prohax) (Jonathan Bowers)

    • Cartesian coordinates

    The Cartesian coordinates for the 1920 vertices of a steriruncic 6-cube centered at the origin are coordinate permutations:

    (±1,±1,±1,±1,±3,±5)

    with an odd number of plus signs.

    Alternate names

  • Runcicantitruncated demihexeract/6-demicube
  • Great prismated hemihexeract (Acronym gophax) (Jonathan Bowers)

    • Cartesian coordinates

    The Cartesian coordinates for the 5760 vertices of a steriruncicantic 6-cube centered at the origin are coordinate permutations:

    (±1,±1,±1,±3,±5,±7)

    with an odd number of plus signs.

    There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique:

    References

    Steric 6-cubes Wikipedia
    (Text) CC BY-SA